Sherlock Holmes is Derek Flint's Musical Sidekick

The sidekick: that secondary character that flanks a main character, paralleling most of the primary hero's moves. From Frank Miller's 1986 graphic novel The Dark Knight Returns, here's a visual example of sidekick trailing, mid-leap. 

Twenty years earlier saw the release of Our Man Flint, the American spoof of James Bond with James Coburn as the impossibly talented Derek Flint. Composer Jerry Goldsmith provided the score. In his main title music, the main theme is first presented in E minor by the guitar, which is also the principal key and instrument of Bond's main theme. The orchestra then picks up the main theme in A minor. The transcription below shows both this A-minor presentation of the melody and an inner voice that mostly follows the main theme's melody down a sixth.

This particular brand of chromaticism for cat-and-mouse games between masterminds has resurfaced in various places in the last fifty years, like in Ennio Morricone's theme for Al Capone from The Untouchables (1987) and Michael Giacchino's end title music for the TV show Alias (2001-2006). Here's a more recent version that returns to the east side of the Atlantic: the inner voice of Goldsmith's melody strongly resembles the A-minor melody for a central theme from BBC's Sherlock (2010-) with Benedict Cumberbatch in the title role and Michael Price and David Arnold as the show's composers.